The Story of the Telegrapher's Equations - from diffusion to a wave. 

Videos that provide historical context and motivations is so helpful in understanding the mathematics. Most mathematical texts and courses just jump straight into the analysis.

I never heard this, as an EE. Heavyside = An Incredible genius. With no training at all.

Mesmerizing! Great work! I was certainly upset when I noticed that the video is over. One can only ask for more and more of such finesse

My dad took his final exams at Cambridge in 1934. He had been a radio enthusiast since his boyhood and, at Cambridge, had taken Professor Turner's course on radio. One of the questions in the final exam was on heat diffusion. My dad said that he simply wrote "Using the telegraph equation, well known to electrical engineers, the solution can immediately be written as xxx". In view of the marks he was given for the entire exam, it was clear that his answer had been accepted as correct.

Fun fact: Heaviside formulated Maxwell’s equations into the vector description equations we still use today. He also discovered Gravitomagnetism - equivalent to weak-field General Relativity - thirty years before Einstein.

It is perhaps mind blowing that Lord Kelvin's cable theory is the basis of computational Neuroscience, where models of neurons (and their elongated "processes") are based on on the very same math.

I studied electrical engineering and I never knew, that Heaviside came up with this function. I'm only familiar with his name from the step function. You summerized this complicated work really well. Even for me it was still a bit too much to digest in a short time. I need to watch this again :)

Check out "The Forgotten Genius of Oliver Heaviside: A Maverick of Electrical Science" by Basil Mahon.

Beautiful recap. You have a gift. Keep it up😊

Heaviside with his 200 IQ, casually saving the Western Civilization and changing its course. Not all heros wear capes

Excellent video. Heaviside is unfortunately obscure despite his role as the father of electrical engineering.

I believe Heaviside also proposed the existence of an ionosphere and the E-layer was named after him until recent years.

Most people don't know that Heaviside invented the first Tunnel Diode, although he didn't actually know the mechanism. It was the steel needle in the pool of mercury with olive oil on top. It's not a semiconductor diode; it's an MIM tunnel diode- a "metal-insulator-metal diode". The olive oil coats the tip if the steel needle and is the barrier the electrons tunnel through...

Thanks for this video! to be fair the telegrapher eqs should be called today Heaviside equations, is great that more people are showing some of the great things that this genius did and making him more known at least between the electrical engineers community, its so sad that like 20 years before his dead he didnt take the opportunity to work on antennas, im sure he would achieved a very great progress in antenna theory like he did with other EM topics.

I accidentally clicked on this, and found it absolutely fascinating.

Excellent video!! I've been teaching electromagnetic at the college level for 45 years and thought I knew a lot about Heaviside's contributions to electromagnetics and mathematics, but this video wove his story with Lord Kelvin's in a way that I hadn't seen before. Very nicely done! One thing I don't understand. I was aware that Heaviside was not "educated." Fine. But if that be so, how does an "uneducated" person walk through a library, see a copy of Maxwell's Treatise, and get ANYTING out of it. I guarantee there are Ph.D.s in the sciences today that couldn't hang tough with Maxwell. In fact, I do know from an excellent book (Heaviside: Sage in Solitude by Paul Nahin) that almost no one in Maxwell's day could read it either. Granted, Heaviside had a couple years of practical experience in telegraph under his belt at this time, but it's beyond me how someone, anyone!, without a formal education in mathematics could possibly understand enough to understand the possibilities of Maxwell's work. I guess the answer is simple: he must have been a genius!

I feel that the video ended a minute too early - you introduce the problem of the transatlantic cable, but miss out Heaviside's invention of the loading coil that solved the problem

I knew of the genius of Heaviside (whose work essentially invented the "Dirac function" although never given credit for it) and his use of Laplace transforms, but this description of the inspiration and derivation of Fourier analysis was new to me. As well new was Heaviside's specific application of Fourier's decomposition.

An interesting property of Fourier's heat equation is that a small disturbance is propagated instantaneously to all distances , effectively traveling faster than the speed of light. The addition of inductance resulting in the telegrapher equation (which is a wave equation) nicely resolves this problem.

Epic - a lot of work in that presentation and a good breakdown of historical progress.

Excellent video. Minor point: "phenomena" - plural; "phenomenon" - singular.

Wow! When I did cable fault location in the 70s and 80s using the "echo location" technique, I did not realize (or was told) that this is all about Fourier's equations (and the series). So, you do learn stuff later in life! 😀

It seems like Heaviside was describing unwanted signal reflections. The “cure” is to make the impedance of the Signal Source, and the impedance of the Transmission Line, and the impedance of the Line Termination ALL possess the same value of impedance.

One of the difficulties with that first cable was, because of the lost of signal, the conventional solution was to increase the input voltage - burning out the cable! I believe Thompson used a Wheatstone bridge to get much greater sensitivity, thus avoiding the 'burn out. problem.

Thanks for talking about him and for teaching me how his last name is pronounced. AFAIK, Heaviside was an electric engineer - though I'm not sure the profession existed formally at the time. The Laplace Transform for the Step Function and Impulse Function are amazing! They were only formally proved in the late 50s and early 60s.

EXCELLENT animation of terminated transmission line! Brings back fond memories. I first made that work w/Apple-II, in assembler, with game paddles as the signal generator. My wave equations were 8-bit, with L and C values of one and two, IIRC. I think it was 1991 or so. (I made a diffusion version first, RC only, before later using zero ohms and adding induction. Also, with LC and some resistive loss, you get naturally-occuring dispersion, slower short-wavelengths, looking like spreading ripples on a pond surface.)

Very well presented. This video provides the historical context and interdisciplinary framework of this important discovery. The mysteries of inductance were still being discovered 50 years after Faraday.

The cover of Paul Nahin's book on Oliver Heaviside is shown at 7:56 of the video. Nahin in 2020 wrote a book on the topic explored in this video. The title is 'Hot (from the Mathematics of Heat) Molecules, (to the Development of the) Cold (Trans-Atlantic Telegraph Cable) Electrons. It is a story book with plenty of Fourier mathematics. Nahin also has a separate book, Transients for Electrical Engineers (2019), emphasizing the Laplace Transform solution for partial differential equations. The last part of the book is about the solution of the Telegrapher Equation and how programs like Matlab can make life easy for the modern analyst. It also explains why the Laplace Transform replaced Heaviside's earlier operator method of solution. It took 10 years but by the 1950's engineers started using Laplace Transforms exclusively. If you love math and stories you are in for a treat from all 3 books.

great job love to see what other work you create!

Beautiful video. Thank you. Just one comment: one phenomenon, two phenomena. This error aside, an excellent exposition.

This is a video thet I was looking for years! Big thanks!

Wow amazing video

Top notch quality!

Really nice explanation of Fourier series ❤

Phenomenal work!

Subscribed in hope that there will be parts 2, 3, .... to follow. On a different note, I have a great problem accepting that there are people without formal education who surface in human history every now and then, who come up with exceptional works and solutions to problems which all the formally trained people before them were unable to sort out. Although Heavyside was not born in a "privelaged" family doesn't mean that there was no intelligent members in his family who had the knowledge which allowed young Oliver to benefit from. From this video it seems that there was at least one. Thank you, great channel. Hope to see more especially on Mr Heavyside.

Never underestimate, a man with focus and a Chief Aim…

Great video, glad I found your channel. When I was learning this topic at school, it was always very difficult to understand. There is a lot in my education that seems missing that would have made it understandable. Got an IT degree in the US, for context, after going to public school.

Beautiful. Thank you.

Another RU-vid channel revealed that it was Heaviside who “fixed” engineering mathematics by improving upon Hamilton’s quaternions. To do this, Heaviside renamed Convergence to Divergence (so engineers wouldn’t have to install a -1), and created the Dot Product operation and the Cross Product operation, for Vectors.

amazing!

that's freaking awesome!!!!

Fantastic. Now please step in at the end of each video and promote the next video. People want your excellent content! I know I do. Seriously.

Excellent as usual. Thank you. What were the repercussions of Heaviside's work for transatlantic communication?

Incredible video, I've recommended this channel to all my nerd friends.

Super inintéressant ! bravo !

When it comes to "it" Heaviside obviously had it. This begs the question, if his uncle had got him a job in the back office of a merchant bank instead, how would history be different? ps I did two years of a City & Guilds radio and line transmission course back in the day and not once did Heaviside's name come up. Perhaps teaching the history would have piqued my interest and I would not have baled out as I did.

Interesting video, but please skip that music interferenze in the backround, the talk is demanding concentration.

thank you VERY much!

think, that was only 150 years ago, and look where we are now. progress is breathtaking, what will it be like in another 100 years

show this helped to fresh up my shortcomings in school

Nice program 😊

Please go on to explain how Heaviside sought to use "lumped" inductance to improve transatlantic telegraph speeds still further...

I would be interesting to know more about the time domain dynamics of that transatlantic cable. As you describe it, it's clear that the Resistance - Capacitance model based on the diffusion equation predicts what is essentially a low pass filter, slowing down and smoothing out the signal pulses carried from the telegraphy equipment. I also guess that the distributed R & C parameters that might be calculated from the incredibly long time taken to reliably send that message would be far larger than the actual parameters for that cable, maybe that was a clue of a problem in the model. More accurately the Telegraphers equation might, given the actual distributed R -L-C parameters for that cable predict a situation where the transmitted pulses reflect back and forth between the mis-terminated ends of the cable. These pulses would keep echoing back and forth until their energy was dissipated by the cable resistance, Guessing a signal travel time across the Atlantic of about 15ms what was likely happening was that for each pulse sent the operator would have to wait for the echoes to die down before the next one was sent.

Quite the edification

Plz also upload video on how alxender Graham bell invented telephone and how Marconi invented radio.love from Nepal 🇳🇵.

After 24 years, i know finally that Signal propagates in a transmission line like heat does in a metal bar, why nobody told me this in 2000?

well give us the result. How were those equations used to optimise the peeformance of the transatlantic telegraph line.

It is more global even than this. The same equation shapes apply to heat, mass and momentum as well. And that is major coursework in Chemical Engineering. Add to this hyperbolic extensions of trigonometry, and J and Bessel functions that extend all of that, and Fourier, Hamiltonian and Hermitian functions to deconvolve and reconstruct signal structures and you really have something. Then add thermodynamics laws and Maxwell's equations for electrodynamics and you'll soon be cooking with steam.

The singular of "phenomena" is "phenomenon".

Heaviside was also the first to propose relativistic length contraction, one of many brilliant concepts incorrectly attributed to Einstein.

And all this was done without an AVO, a computer and an oscilloscope :-)

The subject, contents and explanation is excellent. Unfortunately due to the background music I was unable to concentrate on the contents and mathematics. Although I tried more than once. During all my university years I never attended a lecture on a physical subject where background music was played. Why ruining such excellent work?

The Algorithm is working today.

Very well done! You should collaborate with Kathy loves physics. I think the results could be amazing.

A wonderful presentation about a man not generally known even nowadays. Please though-the singular for phenomena is phenomenon. Three times a single phenomenon here is rendered as the plural. And proportionate instead of proportional? Oh well-that's how it seems to be nowadays. :-(

The so called Maxwell equations, as used in all modern text books, were actually first derived by Heaviside.

Heaviside's head is as rectangular as his Step Function.

Strange that science even Einstein said time is a illusion correct,so that discounts this method.

7:00 - Buchanan (no "o")

Getting your head around refrigeration etc including Air Conditioning is there is no such thing as cold, only lack of heat, so its about moving heat not supplying cold, the process of pressure drop to move heat energy thereby leaving a state of lack of heat perceived as cold !

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@5:17 - That doesn’t sound right…that means they didn’t figure out the problem till about the year 2000. That’s obviously not true.

Optimum frequency

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for alle ingeniørerne derude begynder festen kl. 9:00

Great history lesson and a starter for a reiteration and reorientation to logarithmic derived projection-drawing symbology. It's time consuming like it was for these people, but only an exercise in what you think you see in superimposed elemental function fields of probabilistic correlations as condensation-coordination, eg the cube in the sphere of Euler's e-Pi-i Unit Circle modulo radial-resonance expectations. An apprenticeship of our personal selves to the omnidirectional-dimensional Origin of inside-outside ONE-INFINITY Singularity-point holography.

Who is your audience?

Excellent! This explanation brings together the great contributions made by Fourier, Thompson (Kelvin) and Heaviside. This is seldom, if ever, done in university courses. The usual victim is Fourier, his diffusion equation is routinely ignored. This introduces serious and costly errors. I have in mind the 'theory' of the climate changing 'Greenhouse Effect'. The error introduced to account for the absorption of energy by the so-called 'Greenhouse gases'(GHgs). Current 'Greenhouse' theory takes no account of the fact that GHgs not only absorb heat (infrared - IR) but also emit IR radiation. The UN/IPCC does not recognise this, claiming that GHgs 'trap' heat (IR radiation). This is very clear from satellite images taken by infrared sensitive cameras on weather satellites.

Same thing twice

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"voltage and current diffuse into the cable, just like heat" -- more proof of the ether

"one man who instantly took to Maxwell". Are you kidding?! He was practically at war with Maxwell. Heaviside defecated on Maxwell's electromagnetism to make his own with gibbs. We've suffered the consequences of his blunder borne out of ignorance of quaternions ever since.